User:Cmloegcmluin/EPD: Difference between revisions
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An '''EPD''', or '''equal pitch division''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Harmonotonic tunings|harmonotonic]] tuning. | {{Editable user page}} | ||
An '''EPD''', or '''equal pitch division''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Harmonotonic tunings|harmonotonic]] tuning. | |||
Because pitch is the overwhelmingly most common musical resource to divide equally, this may be abbreviated to '''ED''', or '''equal division'''. | |||
== Specification == | == Specification == | ||
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== Relationship to other tunings == | == Relationship to other tunings == | ||
=== | === Vs. rank-1 temperaments & equal multiplications === | ||
An n- | An n-EPDp is equivalent to a [[Tour_of_Regular_Temperaments#Equal_temperaments_.28Rank-1_temperaments.29|rank-1 temperament]] of p/n, or an [[Equal-step_tuning#Equal_multiplications|equal multiplication]] of p/n. | ||
=== | === Vs. APS === | ||
One period of an EPD will be equivalent to some [[APS|APS, or arithmetic pitch sequence]], which has had its count of pitches specified by prefixing "n-". Specifically, n-EPDx = n-APS(x/n), for example 12-EPD1200¢ = 12-APS(1200¢/12=100¢). | |||
== Examples == | == Examples == | ||
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! 4 | ! 4 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(1) | |(1) | ||
|1.19 | |1.19 | ||
| Line 46: | Line 49: | ||
|2 | |2 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(2⁰⸍⁴) | |(2⁰⸍⁴) | ||
|2¹⸍⁴ | |2¹⸍⁴ | ||
| Line 53: | Line 56: | ||
|2⁴⸍⁴ | |2⁴⸍⁴ | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(1) | |(1) | ||
|0.84 | |0.84 | ||